4. Prove that the medians of an equilateral triangle are equal.Solution

5. In a Δ ABC, if ∠A = 120° and AB = AC. Find ∠B and ∠C.

Solution

6. In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.Solution

7. The vertical angle of an isosceles triangle is 100°. Find its base angles.Solution

8. In Fig. 10.24, AB = AC and ∠ACD = 105°, find ∠BAC.

Solution

9. Find the measure of each exterior angle of an equilateral triangle.Solution

10. It is given that the base of an isosceles triangle is produced on both sides.Solution

11. In Fig. 10.25, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD.

Solution

12. Determine the measure of each of the equal angles of a right-angled isosceles triangle.OR ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.Solution

It is given that,ABC is right angled triangle where,

∠A = 90°

AB = AC

We have to find ∠B and ∠C.

Since, AB = AC

∠B = ∠C (Isoceles triangle)

Now,

∠A +∠B+∠C = 180 (Property of triangle)

⇒ 90 + 2∠B = 180 (∠B = ∠C)

⇒ 2∠B = 180 - 90

⇒ ∠B = 45

So, ∠B = ∠C = 45

Hence,

∠B = 45° and ∠C = 45°

13. AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.